Hot pixels or random noise?

I just bought a Nikon J1 a few weeks ago and I found a green dot on my LCD screen today. In the end, it turned out to be a hot pixel, though strangely it appears only on my live view but is mapped out on a playback. It's not an LCD dead pixel because when I use manual focus magnification the green dot becomes bigger.

Anyway, I thought to check if there were any more such defects, and I took shots at ISO 3200. However, even at a fast shutter speed of 1/30s, I get the following:

I took a few burst shots but these dots seem to appear randomly. For example I could put my finger on one of these dots in one image, but it wouldn't be there at the exact same place in another image taken just a second later.

Is this normal behaviour or..? At lower ISO speeds it's not noticeable and with high ISO noise reduction I only get a couple of these dots.